def test_line_rotation(self): from clifford.dg3c import up, up_cga1, up_cga2 from clifford.dg3c import einf1, einf2 from clifford.dg3c import e12, e67 from clifford.dg3c import IC1, IC2 theta = np.pi/2 RC1 = np.e ** (-0.5*theta*e12) RC2 = np.e ** (-0.5*theta*e67) Rdcga = (RC1 * RC2).normal() assert Rdcga * ~Rdcga == 1 # Construct a line pnt_vec = np.array([1, 0, 0]) direction_vec = np.array([0, 0, 1]) Lcga1 = IC1 * (up_cga1(pnt_vec) ^ up_cga1(pnt_vec + direction_vec) ^ einf1) Lcga2 = IC2 * (up_cga2(pnt_vec) ^ up_cga2(pnt_vec + direction_vec) ^ einf2) Ldcga = Lcga1 ^ Lcga2 # Construct a second line pnt_vec_rotated = np.array([0, 1, 0]) Lcga1_rotated = IC1 * (up_cga1(pnt_vec_rotated) ^ up_cga1(pnt_vec_rotated + direction_vec) ^ einf1) Lcga2_rotated = IC2 * (up_cga2(pnt_vec_rotated) ^ up_cga2(pnt_vec_rotated + direction_vec) ^ einf2) Ldcga_rotated = Lcga1_rotated ^ Lcga2_rotated # Assert the rotor rotates it assert (Rdcga * Ldcga * ~Rdcga)|up(pnt_vec_rotated) == 0 np.testing.assert_allclose((Rdcga * Ldcga * ~Rdcga).value, Ldcga_rotated.value, rtol=1E-4, atol=1E-6)
def test_up_down_cga1(self, rng): # noqa: F811 """ Test that we can map points up and down from cga1 """ from clifford.dg3c import up_cga1, down_cga1 pnt_vector = rng.standard_normal(3) for i in range(10 if DISABLE_JIT else 100): pnt = up_cga1(pnt_vector) res = down_cga1(100 * pnt) np.testing.assert_allclose(res, pnt_vector) # Assert an error is raised if the point is not 3d with pytest.raises(ValueError): up_cga1([1, 2, 3, 4])
def test_line(self, rng): # noqa: F811 from clifford.dg3c import up, up_cga1, up_cga2 from clifford.dg3c import einf1, einf2, IC1, IC2 # Make a dcga line pnt_vec_a = rng.standard_normal(3) pnt_vec_b = rng.standard_normal(3) Lcga1 = IC1 * (up_cga1(pnt_vec_a) ^ up_cga1(pnt_vec_b) ^ einf1) Lcga2 = IC2 * (up_cga2(pnt_vec_a) ^ up_cga2(pnt_vec_b) ^ einf2) Ldcga = Lcga1 ^ Lcga2 # Assert that it is an IPNS assert Ldcga | up(pnt_vec_a) == 0 assert Ldcga | up(pnt_vec_b) == 0 assert Ldcga | up(0.5 * pnt_vec_a + 0.5 * pnt_vec_b) == 0
def test_line(self): from clifford.dg3c import up, up_cga1, up_cga2 from clifford.dg3c import einf1, einf2, IC1, IC2 rng = np.random.RandomState() # Make a dcga line pnt_vec_a = rng.randn(3) pnt_vec_b = rng.randn(3) Lcga1 = IC1*(up_cga1(pnt_vec_a) ^ up_cga1(pnt_vec_b) ^ einf1) Lcga2 = IC2*(up_cga2(pnt_vec_a) ^ up_cga2(pnt_vec_b) ^ einf2) Ldcga = Lcga1 ^ Lcga2 # Assert that it is an IPNS assert Ldcga | up(pnt_vec_a) == 0 assert Ldcga | up(pnt_vec_b) == 0 assert Ldcga | up(0.5*pnt_vec_a + 0.5*pnt_vec_b) == 0
def test_translation(self, rng): # noqa: F811 from clifford.dg3c import up, up_cga1, up_cga2 from clifford.dg3c import cyclide_ops from clifford.dg3c import eo, e1, e2, e3, einf1, e6, e7, e8, einf2 from clifford.dg3c import IC1, IC2 # Make a dcga line pnt_vec = rng.standard_normal(3) direction_vec = rng.standard_normal(3) Lcga1 = IC1 * (up_cga1(pnt_vec) ^ up_cga1(pnt_vec + direction_vec) ^ einf1) Lcga2 = IC2 * (up_cga2(pnt_vec) ^ up_cga2(pnt_vec + direction_vec) ^ einf2) Ldcga = Lcga1 ^ Lcga2 # Make a dcga translation rotor in direction of the line Tc1 = 1 - (direction_vec[0] * e1 + direction_vec[1] * e2 + direction_vec[2] * e3) * einf1 Tc2 = 1 - (direction_vec[0] * e6 + direction_vec[1] * e7 + direction_vec[2] * e8) * einf2 Tdcga = (Tc1 * Tc2).normal() # Assert the rotor is normalised assert Tdcga * ~Tdcga == 1 # Apply the rotor to the line np.testing.assert_allclose((Tdcga * Ldcga * ~Tdcga).value, Ldcga.value, rtol=1E-4, atol=1E-6) # Apply the rotor to a point on the line np.testing.assert_allclose( ((Tdcga * up(pnt_vec) * ~Tdcga) | Ldcga).value, 0, rtol=1E-4, atol=1E-6) # Construct and ellipsoid at the origin px = 0 py = 0 pz = 0 rx = 3 ry = 1 rz = 2.5 E = sum([ (-2 * px / rx**2) * cyclide_ops['Tx'], (-2 * py / ry**2) * cyclide_ops['Ty'], (-2 * pz / rz**2) * cyclide_ops['Tz'], (1 / rx**2) * cyclide_ops['Tx2'], (1 / ry**2) * cyclide_ops['Ty2'], (1 / rz**2) * cyclide_ops['Tz2'], (px**2 / rx**2 + py**2 / ry**2 + pz**2 / rz**2 - 1) * cyclide_ops['T1'] ]) # Before moving the elipsoid surface is not touching the origin assert E | eo != 0 # Make a dcga translation rotor to move the ellipsoid Tc1 = 1 - 0.5 * rx * e1 * einf1 Tc2 = 1 - 0.5 * rx * e6 * einf2 Tdcga = (Tc1 * Tc2).normal() assert (Tdcga * E * ~Tdcga) | eo == 0 * e1 # Make a dcga translation rotor to move the ellipsoid Tc1 = 1 - 0.5 * ry * e2 * einf1 Tc2 = 1 - 0.5 * ry * e7 * einf2 Tdcga = (Tc1 * Tc2).normal() assert (Tdcga * E * ~Tdcga) | eo == 0 * e1 # Make a dcga translation rotor to move the ellipsoid Tc1 = 1 - 0.5 * rz * e3 * einf1 Tc2 = 1 - 0.5 * rz * e8 * einf2 Tdcga = (Tc1 * Tc2).normal() assert (Tdcga * E * ~Tdcga) | eo == 0 * e1